This monograph provides a concise point of research topics and reference for modeling correlated response data with time-dependent covariates, and longitudinal data for the analysis of population-averaged models, highlighting methods by a variety of pioneering scholars. While the models presented in the volume are applied to health and health-related data, they can be used to analyze any kind of data that contain covariates that change over time. The included data are analyzed with the use of both R and SAS, and the data and computing programs are provided to readers so that they can replicate and implement covered methods. It is an excellent resource for scholars of both computational and methodological statistics and biostatistics, particularly in the applied areas of health.
Author(s): Jeffrey R. Wilson, Elsa Vazquez-Arreola, (Din) Ding-Geng Chen
Series: Emerging Topics in Statistics and Biostatistics
Publisher: Springer
Year: 2020
Language: English
Pages: 192
City: Cham
Preface
Acknowledgments
About the Book
Contents
List of Figures
List of Tables
Abbreviations
Chapter 1: Review of Estimators for Regression Models
1.1 Notation
1.2 Introduction to Statistical Models
1.2.1 The General Linear Model
1.2.2 Generalized Linear Models (GLMs)
1.2.2.1 Modeling Binomial Data
1.2.2.2 Modeling Poisson Data
1.2.3 Transformation Versus GLM
1.2.4 Exponential Family
1.2.4.1 Canonical Links
1.2.5 Estimation of the Model Parameters
1.2.5.1 Standard Errors
1.2.5.2 Wald Tests
1.2.5.3 Deviance
1.2.5.4 Akaike Information Criterion (AIC)
1.2.5.5 Residual Analysis
1.2.5.6 Computer Generated Output (Partial)
1.3 Review of Generalized Method of Moments Estimates
1.3.1 Generalized Method of Moments (GMM)
1.3.2 Method of Moments (MM) Estimator
1.3.2.1 Generalized Method of Moments Estimation
1.3.2.2 Example of GMM Estimator
1.3.2.3 Properties (Hansen, 1982)
1.3.2.4 Computational Issues
1.3.2.5 Two-Step Efficient GMM
1.3.2.6 Iterated GMM Estimator
1.3.2.7 Continuously Updated GMM Estimator
1.3.3 Some Comparisons Between ML Estimators and GMM Estimators
1.3.3.1 Computer Generated Output (Partial)
1.4 Review of Bayesian Intervals
1.4.1 Bayes Theorem
1.4.1.1 Bayesian Analysis
1.4.1.2 Prior Distributions
1.4.1.3 Noninformative Prior
1.4.1.4 Jeffreys’ Prior
1.4.1.5 Conjugate Prior
1.4.1.6 Posterior Distribution
1.4.1.7 Convergence of MCMC
1.4.1.8 Computer Generated Output (Partial)
References
Chapter 2: Generalized Estimating Equation and Generalized Linear Mixed Models
2.1 Notation
2.2 Introduction to Correlated Data
2.2.1 Longitudinal Data
2.2.2 Repeated Measures
2.2.3 Advantages and Disadvantages of Longitudinal Data
2.2.4 Data Structure for Clustered Data
2.3 Models for Correlated Data
2.3.1 The Population-Averaged or Marginal Model
2.3.2 Parameter Estimation of GEE Model
2.3.3 GEE Model Fit
2.3.3.1 Independence Estimating Equations (IEE)
2.3.3.2 How Bad Is It to Pretend That Δi Is Correct?
2.3.3.3 Sandwich Estimator
2.3.4 The Subject-Specific Approach
2.3.4.1 Conditional Method
2.3.4.2 Random Effects
2.3.4.3 Two-Level Nested Logistic Regression with Random-Intercept Model
2.3.4.4 Interpretation of Parameter Estimates
2.3.4.5 Two-Level Nested Logistic Regression Model with Random Intercept and Slope
2.4 Remarks
References
Chapter 3: GMM Marginal Regression Models for Correlated Data with Grouped Moments
3.1 Notation
3.2 Background
3.3 Generalized Estimating Equation Models
3.3.1 Problems Posed by Time-Dependent Covariates
3.4 Marginal Models with Time-Dependent Covariates
3.4.1 Types of Covariates
3.4.2 Model
3.4.3 GMM Versus GEE
3.4.4 Identifying Covariate Type
3.5 GMM Implementation in R
3.6 Numerical Example
3.6.1 Philippines: Modeling Mean Morbidity
3.7 Further Comments
References
Chapter 4: GMM Regression Models for Correlated Data with Unit Moments
4.1 Notation
4.2 Introduction
4.3 Generalized Method Moment Models
4.3.1 Valid Moments
4.3.2 Multiple Comparison Test
4.3.3 Obtaining GMM Estimates
4.4 SAS Marco to Fit Data
4.5 Numerical Examples
4.6 Some Remarks
References
Chapter 5: Partitioned GMM Logistic Regression Models for Longitudinal Data
5.1 Notation
5.2 Introduction
5.3 Model
5.3.1 Partitioned GMM Estimation
5.3.2 Types of Partitioned GMM Models
5.4 SAS Macro to Fit Data
5.5 Numerical Examples
5.6 Some Remarks
References
Chapter 6: Partitioned GMM for Correlated Data with Bayesian Intervals
6.1 Notation
6.2 Background
6.2.1 Composite Likelihoods
6.3 Partition GMM Marginal Model
6.3.1 Partitioned GMM Estimation
6.4 Partitioned GMM Model with Bayesian Intervals
6.5 Properties of Model
6.6 Code for Fit Model
6.7 Numerical Example
6.8 Some Remarks
References
Chapter 7: Simultaneous Modeling with Time-Dependent Covariates and Bayesian Intervals
7.1 Notation
7.2 Introduction
7.3 Background
7.4 Marginal Regression Modeling with Time-Dependent Covariates
7.4.1 Partitioned Coefficients with Time-Dependent Covariates
7.4.2 Partitioned Data Matrix
7.5 MVM Marginal Model with Bayesian Intervals
7.5.1 Simultaneous Responses with Nested Working Correlation Matrix
7.5.2 Special Case: Single Response MVM Models with Bayesian Intervals
7.6 Simulation Study
7.7 Computing Code
7.8 Numerical Examples
7.9 Some Remarks
References
Chapter 8: A Two-Part GMM Model for Impact and Feedback for Time-Dependent Covariates
8.1 Notation
8.2 Introduction
8.2.1 General Framework
8.3 Two-Part Model for Feedback
8.3.1 Stage 1: Model
8.3.2 Feedback of Responses on Time-Dependent Predictors Model
8.4 Coefficients and Interpretation of the Model
8.5 Implementation in SAS: Code and Program
8.6 Numerical Examples
8.7 Remarks
References
Appendix A: Introduction of Major Data Sets Analyzed in this Book
Medicare Data
ADD Health Data
International Food Policy Research Institute in the Bukidnon Province
Chinese Longitudinal Healthy Longevity Survey (CLHLS)
Reference
Index
